A prediction market provides a central place where people may converge to place orders, such as a betting market for placing bets on the outcome of an event or a financial market for placing orders for trading commodities or securities of uncertain value. In a well-functioning market, the resulting prices can reflect a wealth of information about the expected value of the security, which, in ideal circumstances, may represent the sum total of all information available to all traders. In general, prediction markets can provide forecasts for some future events by aggregating information of participants.
When a future event is or can be treated as a continuous random variable, existing prediction market mechanisms may take one of the following two approaches. The continuous random variable may be discretized into a discrete random variable with finite exclusive outcomes and the probability mass function of the discrete random variable may be predicted. Or some statistic of the continuous random variable, such as the expectation, may be directly predicted. In either case, much information about the continuous random variable is not captured by existing prediction markets.
Other mechanisms in combinatorial prediction markets may provide forecasts of future events by attempting to aggregate more information, but result in dividing traders' attention on market information among an exponential number of outcomes of a joint random variable, making the likelihood of finding agreeable bilateral trades remote. In any case, existing combinatorial prediction markets deal with discrete and finite outcome space. Outcome spaces that are continuous or infinite are discretized into finite outcomes that only allow traders to bet on the finite outcomes. Such a restriction on outcome spaces hinders information aggregation. See for example, L. Fortnow, J. Kilian, D. M. Pennock, and M. P. Wellman, Betting Boolean-style: A Framework for Trading in Securities Based on Logical Formulas, Decision Support Systems, 39(1):87-104, 2004; and R. D. Hanson, Combinatorial Information Market Design, Information Systems Frontiers, 5(1):107-119, 2003.
What is needed is a system and method for prediction markets that may allow participants to trade on continuous or countable infinite outcomes that allow participants to express their information more freely. Such a system and method should be able to support traders for dealing with continuous or countably infinite outcome spaces directly in order to get more complete and refined information from traders.